Question

a lens is formed by combining two thin lenses of power +12d and -8d in contact with each other what will be the focal length of combination​

Answer 1

Answer:

Power of a lens is defined as the reciprocal of the focal length, taken in meters.

$\implies \text{Power (in D)} = \dfrac{1}{\text{Focal Length (in m)}}$

According to the question, the powers of the two lens are given to be:

• Lens 1 = + 12 D
• Lens 2 = - 8 D

Calculating the respective focal lengths, we get:

$\implies \text{Focal Length (in m)} = \dfrac{ 1 }{ \text{Power (in D)} }$

$\implies \text{ Focal length of Lens 1} = \dfrac{ 1 }{ \text{Power of Lens 1} }$

$\implies \text{Focal Length of Lens 1} = \dfrac{ 1 }{ 12\:D }\\\\\\\implies \boxed{ \textbf{Focal Length of Lens 1} = \bf{ 0.083\: m}}}$

Similarly for Lens 2, the focal length would be:

$\implies \text{Focal Length of Lens 2} = \dfrac{1}{ -8\: D}\\\\\\\implies \boxed{\textbf{ Focal Length of Lens 2} = \bf{-0.125\: m}}$

The Formula to calculate the Focal length of combination of these 2 lens is:

$\implies \dfrac{1}{ F_{\text{combination}} } = \dfrac{ 1}{F_1} + \dfrac{1}{F_2} + ... \dfrac{1}{F_n}$

where, 'n' is the number of lenses.

Substituting the given information in this formula we get:

$\implies \dfrac{ 1 }{ F_{ \text{combination} } } = \dfrac{1}{0.083} - \dfrac{1}{0.125}\\\\\\\implies \dfrac{ 1 }{ F_{ \text{combination} } } = \dfrac{0.125 - 0.083}{0.083 \times 0.125}\\\\\\\implies \dfrac{ 1 }{ F_{ \text{combination} } } = \dfrac{0.042}{0.010375}\\\\\\\implies \dfrac{ 1 }{ F_{ \text{combination} } } = 4.008 \approx 4 \\\\\\\implies F_{ \text{combination} } = \dfrac{1}{4}\\\\\\\implies \boxed{ \bf{F_{ \text{combination} } = 0.25 m \:\: (or) \:\: 25 cm}}$

Hence the focal length of the combination of two lenses would be 25 cm.

Answer 2

Answer:

Solution :-

As we know that

P = 1/F

• P is the Power
• F is the Focal Length

1)P = 1/+12

P = 1/12

P = 0.083

2)P = 1/-8

P = -0.125 m

Now,

Focal length of combination

1/F(C) = 1/F1 + 1/F2

1/F(C) = 1/0.083 + 1/-0.125

1/F (C) = 1/0.083 - 1/0.125

1/F (C) = 0.042/0.010375

1/F(C) = 4

1/F(C) = 1/4